Overview
- Group
- SmallGroup(1920,235343)
- Rank
- 6
- Schläfli Type
- {2,5,2,8,6}
- Vertices, edges, …
- 2, 5, 5, 8, 24, 6
- Order of s0s1s2s3s4s5
- 120
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (4,5)(6,7);; s2 := (3,4)(5,6);; s3 := ( 9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29);; s4 := ( 8, 9)(10,14)(11,13)(12,15)(16,20)(17,19)(18,21)(22,26)(23,25)(24,27)(28,31)(29,30);; s5 := ( 8,10)( 9,13)(12,16)(15,19)(18,22)(21,25)(24,28)(27,30);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s3*s4*s5*s4*s3*s4*s5*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(31)!(1,2); s1 := Sym(31)!(4,5)(6,7); s2 := Sym(31)!(3,4)(5,6); s3 := Sym(31)!( 9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29); s4 := Sym(31)!( 8, 9)(10,14)(11,13)(12,15)(16,20)(17,19)(18,21)(22,26)(23,25)(24,27)(28,31)(29,30); s5 := Sym(31)!( 8,10)( 9,13)(12,16)(15,19)(18,22)(21,25)(24,28)(27,30); poly := sub<Sym(31)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;